Musculoskeletal diseases affect hundreds of millions of people around the world. Neuromuscular disorders is one important group of these diseases. Prevalence of neuromuscular disorders is about 0.1 – 0.3% in general population [Dee15], which is similar to that of Parkinson’s disease worldwide. What makes these disorders important, however, is the fact that they are typically incurable, leading eventually to death. Their treatment is generally ameliorative, involving changes in lifestyle supported by rehabilitation to improve the quality of patient life.

Osteoporosis, a disease that makes bones fragile, also belongs among musculoskeletal diseases. In the population over 50 years of age, about 30 – 50% of women and 15 – 30% of men [Kan00] will, at some stage, suffer from a fractured bone. In 2010, the annual number of new fractures in the EU was estimated at 3.5 million, comprising approximately 620 000 (17.7%) hip, 520 000 (14.9%) vertebral, 560 000 (16.0%) forearm, and 1 800 000 other fractures [Her13]. Due to changes in population demography, it is expected that by 2025 this number could increase by 28%. In Europe, osteoporosis kills more women annually than breast cancer, mostly as a result of complications following fractures. About 20-24% patients with hip fracture will die of related complications within 12 month; many others will remain impaired – the disability due to osteoporosis is greater than that caused by cancers (with the exception of lung cancer) [Coo93]. Economic burden is enormous: osteoporotic fractures costs the European health system more than 30 billion EUR per year (275 million EUR, i.e., is 7.4 billion CZK, in the Czech Republic) [Sve13]. By 2050 this could double.

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To maximise the effectiveness of the prevention, diagnosis and the treatment of musculoskeletal diseases, a full understanding of the physiology of muscles is required – for example, one needs to understand the role played by different motion activities (e.g., walking, climbing stairs or falling) in the overall risk of bone fracture in order to be able to propose suitable changes in lifestyle. To be useful, this assessment has to be specific to the individual patient. All this is not feasible without a proper modelling technology.

Existing Approaches

An example of musculoskeletal model based on lines of action.
An example of musculoskeletal model based on lines of action.

Although medical imaging, e.g. magnetic resonance imaging (MRI) and computed tomography (CT), can potentially provide all the data from which a complete anatomical model of a patient can be constructed, it is currently impractical (and unethical, considering the amount of imaging that would have to be performed on the patient) to create such a customised model from scratch. One solution lies in constructing a generic musculoskeletal model (using data from cadaver studies) that can be scaled and morphed to fit a patient-specific model, using limited imaging and morphometric data from the patient.

Existing musculoskeletal models can be distinguished into two main groups. First, there are models that represent a muscle by a 3D FEM mesh (e.g., [Lu11, Obe09, and Ble05]). Muscle architectural parameters, such as the direction of the muscle fibres paths, are stored in the cells of this mesh so that when the mesh vertices move in reaction to the external force induced by the movement of the bones, the internal muscle structure also changes, which means that the paths of the muscle fibres are updated. Although a good agreement was found comparing the results with static MRI images taken in different postures, and, therefore, these methods have an impact on research problems (with errors of biomechanical predictions below 5%), their use in clinical contexts is highly impractical mainly because adapting the general model to individual patient is complex easily requiring easily several hours for a highly skilled operator and , once the model is prepared, computing the solution may require several hours even on a supercomputer [Ble05]. A good survey of these approaches can be found in [Lee12].

Next, there are models, e.g., [Aud08, Gar00], that represent a muscle by one or more poly-lines, named lines of action, joining the origin and insertion points of the muscle, i.e., the sites at which the muscle is attached to the bone by a tendon, and passing through a number of predefined via points, fixed to the underlying bone, or wrapping automatically around predefined parametric objects. In essence, a line of action is a representation of the muscle fibres and tendons. An advantage of these models, which makes them so popular in common clinical practice, is their simple adaptation to anatomy of the individual patient and rapid processing speed. However, representing a muscle by a set of ad hoc lines of action provides very limited insight since it lacks many features important in the functioning of muscles. As a result, biomechanical predictions of forces are typically inaccurate. A study [Val12] shows that representing a muscle, especially, a complex one such as gluteus medius, by a single line of action can produce muscle moments errors up to 75%. Naturally, this decreases as the number of lines of actions increases, however, as their specification requires user intervention, it is usual that no more than two lines of action per a muscle are specified in practice.

Our Approach

Our research aims to combine advantages of both existing groups. In our musculoskeletal model [Koh13], the outer shape of a muscle is represented by a triangular surface mesh and the internal structure of the muscle is automatically constructed by a slice-by-slice morphing of the predefined fibre template into the interior of the muscle exploiting a harmonic scalar field constructed on the muscle mesh to find a relationship between the fibre template and the muscle mesh [Koh14]. Alternatively, if the information about the fibres on the surface of the muscle is available, the internal structure can be automatically reconstructed from these fibres using the interpolation method described in [Koh17]. Providing that the surface model of the muscle represents not only the muscle belly but also tendons by which this muscle belly is connected to bones, i.e., it represents muscle-tendon unit, each generated muscle fibre can be considered to be a single line of action. Whilst a muscle in common lines of action models is typically represented by a couple of lines of action only, one could easily generate an arbitrary number of fibres (and thus lines of action) using our decomposition, thus consequently improve accuracy in force estimation in most cases.

The process of constructing the interior of the muscle - its fibres. The alternative process of constructing the interior of the muscle - its fibres.
The process of constructing the interior of the muscle; top slice-by-slice morphing [Koh14], bottom interpolation [Koh17]. 

Laplacian mesh processing is introduced to deform a generic model to a patient-specific model, based on patient-specific landmarks extracted from two orthogonal clinical images and using least-squares error optimization as described in [You13]. Muscle attachment landmarks and motion landmarks in the atlas are also transformed as part of the process. Drift and inter-surface penetrations are prevented by supplementary inter-surface landmarks.

Scaling of the musculoskeletal model.
Bones and muscles of the generic atlas model: (a) before, (b) after Laplacian scaling; (c) shows the fitting of the scaled model to EOS images of the patient.

Three different pathways to wrap the muscles and their fibres (or lines of action) in the patient-specific model around the moving bones have been designed. Mesh skinning and energy minimization model pathways exploits strategy surface-first, particle based model pathway strategy fibres-first.

Our approach.
Workflow of our approach. Green spheres are used at places where more options exist (only one path is to be chosen).

In the former one, the movement of the skeleton triggers the deformation of the surface mesh of the muscle, with muscle volume being conserved [Koh12] and inter-penetration with bones and other muscles avoided [Kel12], governed by the change of automatically constructed skeleton of the muscle [Haj14]. If the skeleton line gets shorter, the muscle must bulge to preserve its volume; if it wraps around an obstacle, the muscle must bend. Only after that the internal structure of the deformed muscle is constructed as described above.

In the fibres-first, the internal structure of the muscle is constructed first. It is transformed into a sets of discrete particles bound by physical forces to maintain the fibrous structure throughout the motion; in its simplest form, this is a mass-spring system. The end nodes are fixed to the bones so that when the bones move, the equilibrium of the system is violated and this triggers a recalculation of the positions of the inner nodes [Jan14]. The deformed shape of the muscle surface can then be determined from the new positions of the particles exploiting mean value coordinates approach [Jan15].

Muscle wrapping.
The deformed iliacus muscle with its skeleton in the rest (green) and the current (blue), i.e., deformed, pose, and the deformed glutes muscle wrapped around the femur bone (avoiding inter-penetration)
Fibres wrapping.
The mass-spring system for gluteus medius and the muscle fibres wrapped around the bones in the current pose (avoiding inter-penetration)

Each pathway has its pros and cons. Mesh skinning can process a single muscle in a couple of milliseconds on a commodity hardware (and, therefore, it is recommended for the first experiments), however, it guarantees neither preservation of muscle volume nor avoidance of interpenetration between muscles and bones, relying thus solely on the proper specification of muscle skeletons in every simulation step. Energy minimization model is able to preserve muscle volume, however, it may suffer from severe inter-penetration in some cases due to its sensitivity to the quality of muscle skeleton. Furthermore, processing times rise to seconds. Finally, particle based model is much slower (times are in minutes) and cannot preserve the muscle volume, however, it avoids any interpenetration.

Optimisation and improvements of these pathways are currently in-progress.


VPHOP hyper-model used in the clinical workflow.

Our musculoskeletal model is a part of VPHOP multiscale patient-specific hyper-model that was developed in the scope of the EC funded project VPHOP: the Osteoporotic Virtual Physiological Human (FP7-ICT-223865), 2008-12, an integrated project involving 21 partners. VPHOP modelling technology makes it possible, in a clinical setting, to assess for each patient individually, the strength of their bones, how this strength is likely to change over time, and the probability that they will overload their bones during daily life in 10 years period in the dependency on the chosen treatment. Retrospective clinical assessment of VPHOP hyper-model suggests that a clinical estimate with a predictive accuracy of 80% or even better can be expected, which is a significant improvement over the current standard of care (based on FRAX tool and DXA bone densitometry) that is able to correctly diagnose only up to 60% patients. This improvement represents an important reduction of the number of osteoporotic fractures per year should this technology become commonly available. The return on investment in VPHOP technology is 3 years for large private osteoporotic centre. On the society level, the return on investment is in one year.

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Screenshots and videos

Final model.
Final model.
Musculoskeloskeletal modelling - process
Muscle decomposition


The latest release version of our musculoskeletal model is available for non-commercial use providing it is properly cited in all publications regarding the work in which it is used. For the citation, please use: Kohout J, Clapworthy GJ, Zhao Y, Tao Y, Gonzales-Garcia G, Dong F, Kohoutová E. Patient-specific fibre-based models of muscle wrapping. Interface Focus 2013, Royal Society Publishing; 3(2):1-8.

There is also a method that constructs the muscle fibre in the interior of a muscle based on the knowledge of serveral fibres sampled on the surface of the muscle. For the citation, please use: Kohout J, Cholt D. Automatic reconstruction of the muscle architecture from the superficial layer fibres data. Computer Methods and Programs in Biomedicine 2017,150:85-95.


[Aud08] Audenaert A, Audenaert E. Global optimization method for combined spherical-cylindrical wrapping in musculoskeletal upper limb modelling. Computer Methods and Programs in Biomedicine 2008, 92(1): 8–19.

[Ble05] Blemker SS, Delp SL. Three-dimensional representation of complex muscle architectures and geometries. Annals of Biomedical Engineering 2005, 33(5):661–673.

[Coo93] Cooper C, Atkinson EJ, Jacobsen SJ, et al. Population-based study of survival after osteoporotic fractures. American Journal of Epidemiology 1993, 137(9):1001-1005.

[Dee15] Deenen JCW, Horlings CGC, Verschuuren JJGM, et al. The Epidemiology of Neuromuscular Disorders: A Comprehensive Overview of the Literature. Journal of Neuromuscular Diseases 2015, 2(1): 73-85.

[Gar00] Garner B, Pandy M. The obstacle-set method for representing muscle paths in musculoskeletal models. Computer Methods in Biomechanics and Biomedical Engineering 2000, 3(1): 1–30.

[Haj14] Hájková J, Kohout J. Human Body Model Movement Support: Automatic Muscle Control Curves Computation. In: Combinatorial Image Analysis, Lecture Notes in Computer Science 2014, 8466: 196-211.

[Her13] Hernlund E, Svedbom A, Ivergard M, Compston J, et. al. Osteoporosis in the European Union: medical management, epidemiology and economic burden. Archives of Osteoporosis 2013, 8(1-2): 136.

[Kan00] Kanis JA, Johnell O, Oden A, et al. Long-term risk of osteoporotic fracture in Malmo. Osteoporosis International 2000, 11(8): 669-674.

[Jan14] Janák T, Kohout J. Musculoskeletal System Modelling. In: Proceedings of GRAPP 2014, January 2014, Lisboa, Portugal, pp. 301-311

[Jan15] Janák T, Kohout J. An efficient mesh deformation method for mass-spring muscle models. In IEEE 15th International Conference on Bioinformatics and Bioengineering (BIBE), November 2-4, 2015, Belgrade, Serbia, pp. 1-6.

[Kel12] Kellnhofer P, Kohout J. Time-convenient Deformation of Musculoskeletal System. In: Proceedings of Algoritmy 2012, September 9-14, 2012, Vysoké Tatry, Podbanské, Slovakia, pp. 239-249.

[Koh12] Kohout J, Kellnhofer P, Martelli S. Fast Deformation for Modelling for Musculoskeletal System. In: Proceedings of GRAPP 2012, February 2012, Rome, Italy, pp. 16-25.

[Koh13] Kohout J, Clapworthy GJ, Zhao Y, Tao Y, Gonzales-Garcia G, Dong F, Kohoutová E. Patient-specific fibre-based models of muscle wrapping. Interface Focus 2013, Royal Society Publishing; 3(2):1-8

[Koh14] Kohout J, Kukačka M. Real-Time Modelling of Fibrous Muscle. Computer Graphics Forum 2014, 33(8): 1–15.

[Koh17] Kohout J, Cholt D. Automatic reconstruction of the muscle architecture from the superficial layer fibres data. Computer Methods and Programs in Biomedicine 2017,150:85-95.

[Lee12] Lee D, Glueck M, Khan A, Fiume E, Jackson K. Modeling and simulation of skeletal muscle for computer graphics: A survey. Foundations and Trends in Computer Graphics and Vision 2012, 7(4): 229–276.

[Lu11] Lu YT, Zhu HX, Richmonds S, Middleton J. Modelling skeletal muscle fibre orientation arrangement. Computer Methods in Biomechanics and Biomedical Engineering 2011, 14(12): 1079–88.

[Obe09] Oberhofer K, Mithraratne K, Stott NS, Anderson IA. Anatomically-based musculoskeletal modeling: Prediction and validation of muscle deformation during walking. Visual Computer 2009, 25(9): 843–851.

[You13] Zhao Y, Clapworthy GJ, Kohout J, Dong F, Tao Y, Wei H, McFarlane N. Laplacian Musculoskeletal Deformation for Patient-Specific Simulation and Visualisation. In: Proceedings of 17th International Conference on Information Visualisation (IV2013) London, 15-18 July, 2013, London, UK, pp. 505-510.

[Sve13] Svedbom A, Hernlund E, Ivergard M, et al. Osteoporosis in the European Union: A compendium of country-specific reports. Archives of Osteoporosis 2013, 8(1-2):137.

[Val12] Valente G, Martelli S, Taddei F, Farinella G, Viceconti M. Muscle discretization affects the loading transferred to bones in lower-limb musculoskeletal models. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 2012, 226(2): 161–169.